Concerning demographic limitations on the population growth rate of West Australian (breeding stock D) humpback whales

The upper bound of 0.126 on the maximum demographically possible annual population growth rate for humpback whales that is currently imposed on age-aggregated assessment models for this species, is based on an analysis that assumes steady age structure. It is conceivable that transient age-structure effects could admit greater population growth rates than suggested by such a bound for short periods. This possibility is addressed by developing an age-structured population model in which possible density dependent changes in pregnancy rate, age at first parturition and natural mortality are modeled explicitly, and allowance is made for the possibility of senescence. The model is applied to the case of the west Australian humpback whale population (breeding stock D), for which breeding ground surveys over the 1982-1994 period provide a point estimate of 0.10 for the annual population growth rate. Results based upon the breeding population surveys estimate of abundance of 10032 in 1999 suggest that 0.12 is the maximum feasible annual rate of increase for this stock over 1982-1994 if it is closed. This result is based on essentially the same parameter choices as led to the earlier r = 0.126 bound, viz. that in the limit of low population size the age at first parturition approaches 5 years from above, the annual pregnancy rate 0.5 from below, and the annual natural mortality rate 0.01 from above.